Doubt it is the airline. Not entirely sure how JFK is configured but usually you have gates that are domestic or international, so they were probably assigned a domestic gate by the airport.

Alternatively some airports have gates which are domestic and international and have staff opening different doors which go to different passageways depending on where the flight has came from.

I assume it could be a series of errors in which both airport and airline/pilots are to blame.

One of the most maddening parts of travel SNAFUs is how they use this blame-shifting to avoid responsibility. I've encountered this numerous times flying in/out of JFK/LGA/EWR where they'll just blame each other endlessly and/or the weather without there being any truth to it. Insert Spiderman-pointing-meme here.

Every international gate can be a domestic gate in the US -- you just exit into the terminal via the same door you would board the plane from. It is pretty common to deplane a domestic flight at an international-capable gate at JFK and basically every other large airport in the US.

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The headline is worded pretty terribly as well. Customs controls the flow of goods, immigration controls the flow of people. Skipping customs is hardly a big deal, there’s nothing you can do to fix it at least. Entering a country without being processed by immigration is more likely to cause problems for the passengers. Though probably not in the US, there seems to be little control on outgoing passengers there.